Screw modifier not following spiral curve
The problem is caused by the mesh and the curve not having the same origin.
Once the objects are aligned, the spiral has constant width.



One way to make the objects share the origin is:


Select the curve, press Shift+S and choose “Cursor to Selection”
Select the mesh, press Shift+S, choose “Selection to Cursor”


Kudos to David for finding the solution for an answer to a similar question